CHAPTER III. 



CONDUCTORS AND CONDENSERS. 



73. BY a conductor, as previously explained, is meant any body or 

 system of bodies, such that electricity can flow freely over the whole. When 

 electricity is at rest on such a conductor, we have seen ( 44) that the charge 

 will reside entirely on the outer surface, and ( 37) that the potential will 

 be constant over this surface. 



A conductor may be used for the storage of electricity, but it is found 

 that a much more efficient arrangement is obtained by taking two or more 

 conductors generally thin plates of metal and arranging them in a certain 

 way. This arrangement for storing electricity is spoken of as a " con- 

 denser." In the present Chapter we shall discuss the theory of single 

 conductors and of condensers, working out in full the theory of some of the 

 simpler cases. 



CONDUCTORS. 



A Spherical Conductor. 



74. The simplest example of a conductor is supplied by a sphere, it 

 being supposed that the sphere is so far removed from all other bodies that 

 their influence may be neglected. In this case it is obvious from symmetry 

 that the charge will spread itself uniformly over the surface. Thus if e is 

 the charge, and a the radius, the surface density <r is given by 



total charge e 



~ total area of surface 4<7ra 2 ' 



The electric intensity at the surface being, as we have seen, equal to 

 47rcr, is e/a 2 . 



From symmetry the direction of the intensity at any point outside the 

 sphere must be in a direction passing through the centre. To find the 

 amount of this intensity at a distance r from the centre, let us draw a sphere 

 of radius r, concentric with the conductor. At every point of this sphere 

 the amount of the outward electric intensity is by symmetry the same, say R, 



